I have the same problem, and wasn't able to fix it, as qmail maintainers are not interested in SELinux, or so I was told in chat. It is too bad I cannot install grsecurity (for some reason, system with patched kernel won't boot) and cannot afford ART's great pre-compiled kernels right now, because this leaves SELinux as my only option to add a bit of protection to some critical services.

Chrooting apache in Plesk seems also not to be an easy thing to do.

Anyhow, I investigated this permission problems a bit, and it seems that the domain transition specified in plesk.te (Plesk SELinux policy) is causing some trouble with sendmail when it is used from a php script.

Yes, this can be done. You are basically using the SMTP server instead than sendmail in this way, if I am not wrong.

But SWSoft should also update their policy, as the problem seems to lie in the domain transition of the plesk.te policy from httpd script type to sendmail type. It is like sendmail is trying to perform actions that should be done by httpd.